Optimization of the High Nonlinear S-Boxes Generation Method

The known method of high nonlinear S-boxes generation based on the gradient descent [Kazymyrov, O. V.: Methods and Techniques of Generation of Nonlinear Substitutions for Symmetric Encryption Algorithms. The thesis for the scholarly degree of candidate of technical sciences, speciality 05.13.21 - - Information security systems, Kharkiv National University of Radioelectronics, Kharkiv, 2014. (In Russian)] requires consecutive applications of several criteria for each formed substitution. This paper presents an improvement of the considered method by the appropriate selection of the criteria application order which decreases the required computational power for S-box generation. The proposed modification allows generation of a byte substitution with nonlinearity 104, algebraic immunity 3 and 8-uniformity within approximately 30 minutes of a single PC running time.